Estimates of Generalized Hessians for Optimal Value Functions in Mathematical Programming

Abstract We consider the optimal value function of a parametric optimization problem. A large number publications have been dedicated to study continuity and differentiability properties function. However, aspect works in current literature has mostly limited first order analysis, with focus on estimates its directional derivatives subdifferentials, given that is typically nonsmooth. With progress made last two three decades major subfields such as robust, minmax, semi-infinite bilevel optimization, their connection function, there need for second analysis generalized this This could enable development robust solution algorithms, Newton method. The main goal paper provide Hessian Our results are based handy tools from namely Lagrange multiplier mappings, which completely detailed either well-known or can easily be obtained.